An optimal multistep predictor based on the 1-step-ahead predictor is presented. It is shown that parallel predictors need not be implemented in order to predict the output of some stochastically disturbed system over a future horizon of sampling instants. When the parameters are not known the self-tuning property of the 1-step ahead predictor combined with a least-square recursive identification algorithm is inherited by the future predictions obtained on its bases. The structure complexity of the problem can thus be reduced to its minimal expression, i.e., the 1-step-ahead step-tuning predictor.

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